STATS

Statistics

a set of tools to help us organize data, summarize data, and interpret data.

Data

set of systematic measurements or observations.

Data (plural)

measurements or observations.

Data set

collection of measurements or observations.

Datum (singular)

single measurement or observation and is commonly called score or row score.

Interpret data

determine the relation between two or more variables.

Variables

a characteristic or condition of an object or human that has different values for different individuals.

Population

the group of all people or objects that we are interested in.

Population parameter

a value that describes a population.

Sample

a subset of the population.

Random sample

if the sample is selected so that each member of the population has an equal chance of being selected.

Sample statistic

a value that describes a sample.

Descriptive statistics

allow us to summarize, organize, and simplify data.

Measures of central tendency

tell us about the average value of the mean, median, and mode.

Measure of dispersion

tell us how similar the data are to the average value of range, semi-interquartile range, and standard deviation.

Inferential statistics

allow to study samples and then make generalizations about the population from which they were selected.

Sampling error

the discrepancy between a sample statistics and a population parameter.

Correlational method

involves measuring two or more variables to determine whether there is a relationship between them.

Correlational study

one that is designed to determine the correlation, or degree of relationship, between two traits, behaviors, or events.

Correlation

when the data from a correlational study consists of numerical scores, the relationship between the two variables is usually measured and described.

Calculating correlations:

• Pearson Product Moment Correlation Coefficient (r_)

• Scatterplot

• Positive Correlation

• Negative Correlation

• Curvilinear Relationship

• Outliers

Scatterplot

demonstrates the direction of a correlation.

Positive correlation

as one variable increases, the other variable increases too.

Negative correlation

as one variable increases, the other variable decreases.

Curvilinear relationship

occurs when the ratio of change between two variables is not constant.

Outliers

extreme scores that usually affect correlations by disturbing trends in data.

Properties of a Correlation:

• Linearity

• Sign

• Magnitude

• Probability

Linearity

how the relationship between x and y can be plotted as a line or a curve.

Sign

refers to whether the correlation coefficient is positive or negative.

Magnitude

the strength of the correlation coefficient, ranging from -1 to +1.

Probability

the likelihood of obtaining a correlation coefficient of this magnitude due to chance.

Chi-square test

relationships between variables of on-numerical data.

Limitations of the Correlational Method:

• Coefficient of determination (r2)

• Causal direction

• Bidirectional causation

• Third variable problem

Coefficient of determination

estimates the amount of variability that can be explained by a predictor variable.

Causal direction

we cannot be sure, which the variable is the cause and which is the effect.

Bidirectional causation

both variables could cause the other variable.

Third variable problem

there could be some other variable that is the cause that is yet to be measured.

Experiments

are a special type of research in which all the variables except the independent and dependent variables are held constant.

Independent variable

the variable that the researcher systematically manipulates.

Dependent variable

the variable that the researcher measures or records.

Characteristics unique to Experiments:

• Manipulation

• Control

• Comparison

• Measurement

Manipulation

researcher manipulates one variable by changing its value from one level to another.

Control

researcher must exercise control over the research situation to ensure that other extraneous variables do not influence the relationship being examined.

Confounded

it is impossible to reach an unambiguous conclusion.

Participant variables

characteristics such as age, gender, and intelligence that vary from one individual to another.

Environmental variables

characteristics of the environment such as lighting, time of day, and weather conditions.

Random assignment

each participant has an equal chance of being assigned to each of the treatment conditions.

Matching

matching the levels of the variable across treatment conditions to ensure equivalent groups or equivalent environments.

Holding variables constant

all individuals in the experiment could be observed in the same room, at the same time of day, by the same researcher.

Control condition

the group that does not receive the treatment.

Treatment condition

the group that receives the treatment.

Quasi-experiment

similar to a real experiment except that the participants have been assigned to the various groups based on some characteristic of the participant.

Quasi means

“seeming like”

Constructs

are internal attributes pr characteristics that cannot be directly observed but are useful for describing and explaining behavior.

Operational definition

identifies a measurement procedure for measuring an external behavior and uses the resulting measurements as a definition and a measurement of a hypothetical construct.

Discrete variable

consists of separate, indivisible categories. No values can exist between two neighboring categories.

Continuous variable

there are an infinite number of possible values that fall between any two observed values. Divisible into an infinite number of fractional parts.

Real limits

the boundaries of intervals for scores that are represented on a continuous number line.

Lower real-limit

bottom of the interval.

Upper real-limit

top of the interval.

Levels of Measurement:

• Nominal scale

• Ordinal scale

• Interval scale

• Ration scale

Nominal scale

a set of categories that have different names in no particular order.

Ordinal scale

a set of categories organized in an ordered sequence.

Interval scale

consists of ordered categories that are all intervals of exactly the same size.

Ration scale

an interval scale with the additional feature of an absolute zero point.

Frequency distributions

an organized tabulation of the number of individuals located in each category on the scale of measurement.

Percentile rank

a particular score is defined as the percentage of individuals in the distribution with scores at or below the particular value.

Symmetrical distribution

it is possible to draw a vertical line through the middle so that one side of the distribution is a mirror image of the other.

Skewed distribution

the scores tend to pile up toward one end of the scale and taper off gradually at the other end.

Tail of the distribution

the section where the scores taper off toward one end of a distribution.

Positively skewed distribution

the tail points toward the positive end of the x-axis.

Negatively skewed distribution

the tail points to the left end of the x-axis.

Cumulative frequency distributions

listing the number of scores that are less than or equal to the class. useful for calculating the percentile rank.

Two parts of Quantitative Observation:

1. Stem plots

2. Leaf plots

Stem plots

first digit/s of the number.

Leaf plots

the digit after the stem.

Kurtosis

volume of scores in tails and shoulders of the distribution.

Types of Kurtosis:

• Leptokurtic

• Mesokurtic

• Platykurtic

Leptokurtic

tails are thick and shoulders are thin.

greater concentration of scores around the mean.

Mesokurtic

both tails and shoulders are neither too thick nor too thin.

moderate concentration of scores around the mean.

Platykurtic

tails are relatively light, while shoulders are thick.

lower concentration of scores around the mean.

Modality

the number of popular scores in a distribution.

indicated by the number of distinct peaks.

Types of Modality:

• Unimodal

• Bimodal

• Multimodal

Unimodal

one popular, one peak.

Bimodal

two popular, two peaks.

Multimodal

many popular, many peaks.

Central tendency

a statistical measure to determine a single score that defines the center of a distribution.

Mean

the sum of the scores divided by the number of scores.

Median

the point on the measurement scale below which 50% of the scores in the distribution are located.

Mode

the score or category that has the greatest frequency.

Variability

provides a quantitative measure of the differences between scores in a distribution and describes the degree to which the scores are spread out or clustered together.

Quartiles

the scores having percentile ranks of 25%, 50%, 75%, and 100%, which are termed the first, second, third, and fourth quartile, respectively.

Interquartile Range (IQR)

the distance between the X values that correspond to the first (Q1) and third (Q3) quartiles. It reflects the range for the scores that fall in the middle 50% of the distribution.

Deviation or deviation score

the difference between a score and the mean.

Variance

the average squared distance from the mean.

Standard deviation

the square root of the variance and provides a measure of the standard, or average distance from the mean.